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The hyperbolic Radon transform has a long history of applications in seismic data processing because of its ability to focus/sparsify the data in the transform domain. Recently, deconvolutive Radon transform has also been proposed with an improved time resolution which provides improved processing results. The basis functions of the (deconvolutive) Radon transform, however, are time-variant, making the classical Fourier based algorithms ineffective to carry out the required computations. A direct implementation of the associated summations in the time–space domain is also computationally expensive, thus limiting the application of the transform on large data sets. In this paper, we present a new method for fast computation of the hyperbolic (deconvolutive) Radon transform. The method is based on the recently proposed generalized Fourier slice theorem which establishes an analytic expression between the Fourier transforms associated with the data and Radon plane. This allows very fast computations of the forward and inverse transforms simply using fast Fourier transform and interpolation procedures. These canonical transforms are used within an efficient iterative method for sparse solution of (deconvolutive) Radon transform. Numerical examples from synthetic and field seismic data confirm high performance of the proposed fast algorithm for filling in the large gaps in seismic data, separating primaries from multiple reflections, and performing high-quality stretch-free stacking. 相似文献
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Acceleration time histories of horizontal earthquake ground motion are obtained by inverting the discrete Fourier transform, which is defined by modelling the probability distribution of the Fourier phase differences conditional on the Fourier amplitude. The Fourier amplitude spectrum is modelled as a scaled, lognormal probability density function. Three parameters are necessary to define the Fourier amplitude spectrum. They are the total energy of the accelerogram, the central frequency, and the spectral bandwidth. The Fourier phase differences are simulated conditional on the Fourier amplitudes. The amplitudes are classified into three categories: small, intermediate and large. For each amplitude category, a beta distribution or a combination of a beta distribution and a uniform distribution are defined for the phase differences. Seven parameters are needed to completely define the phase difference distributions: two for each of the three beta distributions, and the weight of the uniform distribution for phase differences corresponding to small Fourier amplitudes. Approximately 300 uniformly processed horizontal ground motion records from recent California earthquakes are used to develop prediction formulas for the model parameters, as well as to validate the simulation model. The moment magnitude of the earthquakes ranges from 5.8 to 7.3. The source to site distance for all the records is less than 100 km. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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本文首次给出了一种利用扫描分析技术与广义S变换时频分析工具相结合求取介质品质因子（Q值）的方法,与传统的Q值估计方法不同,该方法用一系列等效Q值对叠前衰减数据进行粘性补偿偏移,将偏移后的共反射点道集叠加,利用广义S变换求取补偿后叠加道的时频谱和傅立叶峰值频率,以浅层强反射界面子波时频谱为参考,它他深度处地层子波的时频谱特征与之进行比较,当谱宽和峰值频率达到一致作为正确Q值选定标准,确立了宏观介质的等效Q值分析新方法. 相似文献
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Selection of the wavenumbers k using an optimization method for the inverse Fourier transform in 2.5D electrical modelling 总被引：1，自引：0，他引：1
An optimization method is used to select the wavenumbers k for the inverse Fourier transform in 2.5D electrical modelling. The model tests show that with the wavenumbers k selected in this way the inverse Fourier transform performs with satisfactory accuracy. 相似文献
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《Advances in water resources》1998,21(5):385-399
It is often convenient to use synthetically generated random fields to study the hydrologic effects of spatial heterogeneity. Although there are many ways to produce such fields, spectral techniques are particularly attractive because they are fast and conceptually straightforward. This paper describes a spectral algorithm for generating sets of random fields which are correlated with one another. The algorithm is based on a discrete version of the Fourier-Stieltjes representation for multidimensional random fields. The Fourier increment used in this representation depends on a random phase angle process and a complex-valued spectral factor matrix which can be readily derived from a specified set of cross-spectral densities (or cross-covariances). The inverse Fourier transform of the Fourier increment is a complex random field with real and imaginary parts which each have the desired coveriance structure. Our complex-valued spectral formulation provides an especially convenient way to generate a set of random fields which all depend on a single underlying (independent) field, provided that the fields in question can be related by space-invariant linear transformations. We illustrate this by generating multi-dimensional mass conservative groundwater velocity fields which can be used to simulate solute transport through heterogeneous anisotropic porous media. 相似文献
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D. Atchuta Rao H. V. Ram Babu G. D. J. Sivakumar Sinha 《Pure and Applied Geophysics》1982,120(2):365-374
The self-potential anomaly due to a two-dimensional inclined sheets of finite depth extent has been analysed in the frequency domain using the Fourier transform. Expression for the Fourier amplitude and phase spectra are derived. The Fourier amplitude and phase spectra are analysed so as to evaluate the parameters of the sheet. Application of this method on two anomalies (synthetic and field data) has given good results. 相似文献
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不规则采样地震数据的重建是地震数据分析处理的重要问题.本文给出了一种基于非均匀快速傅里叶变换的最小二乘反演地震数据重建的方法,在最小二乘反演插值方程中,引入正则化功率谱约束项,通过非均匀快速傅里叶变换和修改周期图的方式,自适应迭代修改约束项,使待插值数据的频谱越来越接近真实的频谱,采用预条件共轭梯度法迭代求解,保证了解的稳定性和收敛速度.理论模型和实际地震数据插值试验证明了本文方法能够去除空间假频,速度快、插值效果好,具有实用价值. 相似文献
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不规则采样地震数据会对地震数据的多道处理造成严重影响,将非均匀Fourier变换和贝叶斯参数反演方法相结合,对不规则空间带限地震数据进行反演重建.对每一个频率依据最小视速度确定出重建数据的带宽,然后从不规则地震数据中估计出重建数据的空间Fourier系数.将不规则地震数据重建视为信息重建的地球物理反演问题,运用贝叶斯参数反演理论来估计Fourier系数.在反演求解时,使用共轭梯度算法,以保证求解的稳定性,加快解的收敛速度.理论模型和实际资料处理验证了本方法的有效性和实用性. 相似文献
11.
Continuous wavelet transform,theoretical aspects and application to aeromagnetic data at the Huanghua Depression,Dagang Oilfield,China 总被引：1，自引：0，他引：1
We use the continuous wavelet transform based on complex Morlet wavelets, which has been developed to estimate the source distribution of potential fields. For magnetic anomalies of adjacent sources, they always superimpose upon each other in space and wavenumber, making the identification of magnetic sources problematic. Therefore, a scale normalization factor, a?n, is introduced on the wavelet coefficients to improve resolution in the scalogram. By theoretical modelling, we set up an approximate linear relationship between the pseudo‐wavenumber and source depth. The influences of background field, random noise and magnetization inclination on the continuous wavelet transform of magnetic anomalies are also discussed and compared with the short‐time Fourier transform results. Synthetic examples indicate that the regional trend has little effect on our method, while the influence of random noise is mainly imposed on shallower sources with higher wavenumbers. The source horizontal position will be affected by the change of magnetization direction, whereas the source depth remains unchanged. After discussing the performance of our method by showing the results of various synthetic tests, we use this method on the aeromagnetic data of the Huanghua depression in central China to define the distribution of volcanic rocks. The spectrum slices in different scales are used to determine horizontal positions of volcanic rocks and their source depths are estimated from the modulus maxima of complex coefficients, which is in good accordance with drilling results. 相似文献
12.
Spectral analysis for global navigation satellite system (GNSS) coordinate time series provides a principal tool to understand the intrinsic mechanism that affects tectonic movements. Spectral analysis methods such as the fast Fourier transform, Lomb–Scargle spectrum, evolutionary power spectrum, wavelet power spectrum, etc. are used to find periodic characteristics in time series. Among spectral analysis methods, the chirp Fourier transform (CFT) with less stringent requirements is tested with synthetic and actual GNSS coordinate time series, which proves the accuracy and efficiency of the method. With the length of series only limited to even numbers, CFT provides a convenient tool for windowed spectral analysis. The results of ideal synthetic data prove CFT accurate and efficient, while the results of actual data show that CFT is usable to derive periodic information from GNSS coordinate time series. 相似文献
13.
T. Lee 《Pure and Applied Geophysics》1972,99(1):130-140
Summary The potential field due to a point electrode, above an inclined interface, has been given in the form of a multiple integral, involving modified Bessel functions of the second kind (Skalskaya [9]2). From this formula it is only possible to derive formulae, from which type curves may be computed, for a limited number of cases. By considering the asymptotic expansion of the Hankel transform of this potential function, it is possible to derive results which will permit the complete interpretation of a Schlumberger sounding, carried out in the direction of strike; for an arbitrary angle of dip of the contact. The method of interpretation is suitable for use on a digital computer and has been found to give rapid and reliable results. 相似文献
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Improving seismic resolution is essential for obtaining more detailed structural and stratigraphic information. We present a new algorithm to increase seismic resolution with a minimum of user‐defined parameters. The algorithm inherits useful properties of both the short‐time Fourier transform and the cepstrum to smooth and broaden the frequency spectrum at each translation of the spectral decomposing window. The key idea is to replace the amplitude spectrum with its logarithm in each window of the short‐time Fourier transform. We describe the mathematical formulation of the algorithm and its testing on synthetic and real seismic data to obtain broader frequency spectra and thus enhance the seismic resolution. 相似文献
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非规则采样快速傅里叶变换（NFFT）主要用于快速计算非规则采样数据的频谱及重建.该方法为非规则采样数据频谱重建技术的核心算法.在实现NFFT算法时,高速度和高精度计算是其应用的前提和关键.本文针对二维NFFT计算效率,应用表驱动思路进行改进,将Gauss褶积算子由矩形改进为椭圆以减少计算量,将e指数计算改进为乘法以加快计算速度,并建表解决NFFT算法在地震资料处理中的应用问题.本文同时给出了非规则采样地震数据NFFT谱重建方法.最后本文给出算例验证提出方法的计算速度和精度,和非规则采样地震资料重建结果. 相似文献
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Dr. Werner Meyer-Eppler 《Pure and Applied Geophysics》1951,20(1):1-14
Zusammenfassung Die Spektralanalyse von Schwingungsvorgängen basierte bisher ausschliesslich auf der Fourierschen Funktionaltransformation. Es wird gezeigt, dass diese Art der spektralen Zerlegung nur ein Sonderfall einer allgemeinen Zerlegungsart ist, die auf dem in der periodographischen Analyse vielbenutzten Exhaustionsprinzip beruht. Dieses Prinzip wird auf kontinuierlich variable Verschiebungsweiten ausgedehnt und führt dann zu einer Integraltransformation, die der Fourier-Transformation analog gebildet ist, aber an Stelle der Cosinusfunktion eine Summe von gleichabständigenDirac-Funktionen enthält. Es wird ein Periodograph beschrieben, der eine kontinuierliche Exhaustionsanalyse von Oszillogrammschablonen nach dem optischen Projektionsverfahren ermöglicht.
Summary In the past, spectral analysis of oscillations was based upon the Fourier transform almost exclusively. This spectral decomposition is shown to be merely a special case of a more general type of decomposition which is based upon the concept of exhaustion largely used in periodographic analysis. The exhaustion principle is extended to continuous variable shift periods, the result being an integral transform similar to the Fourier transform, with the exception that the cosine function is replaced by a series of equidistantDirac functions. A periodograph is described which permits continuous exhaustion analysis of oscillogram patterns by means of an optical projection device.相似文献
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Following the depths of investigation of different electrode arrays, given byRoy andApparao (1971) andRoy (1972), a modified pseudo-depth section was suggested for any array byApparao andSarma (1981) as a tool in resistivity and IP prospecting. The tool was used for the interpretation of IP and resistivity anomalies
obtained in a virgin area—Jonnagiri village, Pattikonda Taluq, Kurnool district (A.P.) India. Two of the four bore holes recommended
encountered sulphide mineralization, while the other two met with white altered ashy material at the position of the maximum
anomaly contour in the depth sections.
The drilling results prove the utility of the modified pseudosections in the interpretation of the field data. 相似文献
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Summary The method of relaxation has been applied to the upward continuation of gravity and magnetic data. The method yields results that are more accurate than those given byPeters' scheme, and has certain added advantages. In an alternative approach, the finite Fourier sine transform has been used to reduce an area relaxation to a series of line relaxations. The results, again, are very satisfactory. Only the two-dimensional problem is considered, but, with the help of a digital computor, the method is directly extensible to three-dimensional problems.Presented at the symposium on Geophysical Prospecting held by the Central Board of Geophysics at Baroda (India) between Aug. 15–17, 1959. Published by kind permission of Secretary, Central Board of Geophysics. 相似文献
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Sara B. Akkas Ayse O. Kepenek Meryem Beklioglu Feride Severcan 《Aquatic Sciences - Research Across Boundaries》2010,72(1):71-83
Diel vertical migration (DVM) bioassay-guided Fourier transform infrared spectroscopy can be a prominent non-destructive and
innovative approach for ecological studies. During the characterization of the nature of the fish-exuded kairomone, the peak
area results from the spectroscopic analysis of the control, fish-conditioned (F) and temperature incubated fish-conditioned
(IF) treatments of the DVM bioassays demonstrated that there was a strong correlation between the alterations of the amine
N–H, amide II, amide IV and CH3 asymmetric vibrations, suggesting that both N–H and CH3 molecules may be main components of the fish-exuded kairomone cocktail. The IF treatment, which showed similar results with
the control treatment, supported that the kairomone is inactivated by bacterial biodegradation. The seasonal variations in
the peak areas of the N–H and CH3 bands suggested that DVM response varied seasonally, where migration response developed quickly in warmer seasons. The peak
area of the amine N–H band of the F and IF treatments relative to control conditions can be used as an ideal indicator of
the absence or presence and the promptness of migration, at all seasons. 相似文献